The Role of Sequence Information in Minimal Models of Molecular Assembly

Abstract: Sequence-directed assembly processes - such as protein folding - allow the assembly of a large number of structures with high accuracy from only a small handful of fundamental building blocks. We aim to explore how efficiently sequence information can be used to direct assembly by studying variants of the temperature-1 abstract tile assembly model (aTAM). We ask whether, for each variant, their exists a finite set of tile types that can deterministically assemble any shape producible by a given assembly model; we call such tile type sets "universal assembly kits". Our first model, which we call the "backboned aTAM", generates backbone-assisted assembly by forcing tiles to be added to lattice positions neighbouring the immediately preceding tile, using a predetermined sequence of tile types. We demonstrate the existence of universal assembly kit for the backboned aTAM, and show that the existence of this set is maintained even under stringent restrictions to the rules of assembly. We compare these results to a less constrained model that we call sequenced aTAM, which also uses a predetermined sequence of tiles, but does not constrain a tile to neighbour the immediately preceding tiles. We prove that this model has no universal assembly kit in the stringent case. The lack of such a kit is surprising, given that the number of tile sequences of length N scales faster than both the number and worst-case Kolmogorov complexity of producible shapes of size N for a sufficiently large - but finite - set of tiles. Our results demonstrate the importance of physical mechanisms, and specifically geometric constraints, in facilitating efficient use of the information in molecular programs for structure assembly.